It is known to make use in computer tomography of multi-slice detectors and ray bundles with cone beam geometry for the purpose of scanning objects to be examined, in particular patients. In order to reconstruct a volumetric image including a multiplicity of small volume elements (=voxels), it is necessary to take account of the cone beam geometry in the now three-dimensional image reconstruction.
Such reconstruction algorithms for multi-slice spiral CT can be divided into the two classes of the approximative algorithms and the exact methods. Reference may be made to the following documents as regards the approximative algorithms, each of which is incorporated herein by reference, in its entirety:                M. Kachelrieβ, S. Schaller, and W. A. Kalender, “Advanced single-slice rebinning in cone-beam spiral CT”, Med. Phys. 27 (2000) 754-772        S. Schaller, K. Stierstorfer, H. Bruder, M. Kachelrieβ, and T. Flohr, “Novel approximate approach for high-quality image reconstruction in helical cone beam CT at arbitrary pitch”, Proceedings SPIE 4322 (2001) 113-127        K. Stierstorfer, T. Flohr, H. Bruder, “Segmented Multiple Plane Reconstruction—A Novel Approximate Reconstruction Scheme for Multi-slice Spiral CT”, Proceedings of Intern. Meeting on Fully 3-D Image Reconstruction in Radiology and Nuclear Medicine, Pacific Grove, Calif., USA, October, 30-Nov. 2, 2001, pp. 95-97.        
An overview of the exact methods is set forth in the document by K. Sourbelle, H. Kudo, G. Lauritsch, K. C. Tam, M. Defrise, and F. Noo, “Performance Evaluation of Exact Cone-Beam Algorithms for the Long-Object Problem in Spiral Computed Tomography”, Proceedings of Intern. Meeting on Fully 3-D Image Reconstruction in Radiology and Nuclear Medicine, Pacific Grove, Calif., USA, October, 30-Nov. 2, 2001, pp. 153-156, the entire contents of which are hereby incorporated herein by reference.
Approximative methods are distinguished by a high measure of practicability and flexibility. However, the inclination angle of the measuring rays to the axis of rotation (cone angle) is taken into account only approximately, for which reason the approximation error grows with the cone angle. It may be said overall that, starting from a certain number of detector rows, each approximative method will cause image artifacts, and thus leads to unsatisfactory image results. The exact methods take account without error of the cone-beam-like recording geometry both in the filter step and in the 3D back-projection. They achieve good image results that are independent of the cone angle occurring. However, it is disadvantageous that they are extremely complicated and very inflexible in application.